Lost Universe

Millie Nocturne has one great goal in life: to be the best in the universe - at absolutely everything! But when she tries her hand at being the "best detective," she ends up an unwilling partner with two people who will change her life forever: Kane Blueriver, the psi-blade-wielding master of the starship Swordbreaker, and Canal, the smart-mouthed holographic image of the ship's computer. (myanimelist.net)